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Cluster theory is a significant mathematical success story, with its study having permeated many subjects in mathematics and mathematical physics despite its relatively recent introduction at the turn of the millennium. Indeed, the combinatorics of exchanges, central to Fomin and Zelevinsky’s definition of cluster algebras, has incarnations in contexts as diverse as topology and complex analysis (Skein relations), algebraic geometry (flopping curves) and representation theory (mutations of tilting and silting objects). This ubiquity has led to striking applications including Keller’s proof of the Zamolodchikov periodicity conjecture, Wemyss’ homological minimal model programme, and computations of scattering amplitudes in theoretical physics. In recent years, the north of the UK has become a hotbed of research groups interacting with different aspects of cluster theory – the CLAN network seeks to bring together this growing community and provide regular opportunities for close collaboration.
Raquel Coelho Simões, Lancaster University
Anna Felikson, Durham University
David Pauksztello, Lancaster University
Alexander Shapiro, University of Edinburgh
Pavel Tumarkin, Durham University
Jon Wilson, University of Central Lancashire (Clan Chief)
Emine Yıldırım, University of Leeds
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The CLAN research network is generously supported by the London Mathematical Society via a Scheme 3 grant.
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